Digital serial multiplier

ABSTRACT

A multiplier of a binary number A by a binary number B may be configured to add each term A i B j  with a left shift by i+j bits, where A i  is the bit of weight i of number A, and B j  the bit of weight j of number B. The multiplier may include a first counter associated with the number A and may count modulo n and be paced by a clock. The multiplier may include a second counter associated with the number B and paced by the clock. Switching circuitry may produce the terms A i B j  by taking the content of the first and second counters respectively as weights i and j. Shifting circuitry is configured to shift the content of one of the first and second counters when the other counter has achieved a revolution.

FIELD OF THE INVENTION

The invention relates to binary multipliers, and more particularly, to amultiplier to be incorporated into a built-in self-test device.

BACKGROUND OF THE INVENTION

More and more integrated circuits are equipped with built-in self-testdevices, also called BIST devices. Such devices are often used in thetest phase in the production of integrated circuits. They are designedto assist the test equipment in testing specific functionalities and toreduce the testing time.

Use of a binary multiplier is frequently needed in a BIST device. FIG. 1shows a multiplication calculation methodology used as a basis for manybinary multiplier structures. The aim is to multiply, for example, abinary number A of 4 bits A₀ to A₃, by a binary number B of four bits B₀to B₃. All the partial products or terms A_(i)B_(j), sixteen terms inthe example, are divided into 7 columns, such that each term A_(i)B_(j)is arranged in the column of rank i+j. The ranks of the columnscorrespond to the weights of the result R of the multiplication.

The result R is obtained by adding the binary numbers formed by thejuxtaposed terms of the columns. A column is completed by a 0 when thereis no term. The result thus comprises 7 bits R0 to R6 correspondingrespectively to the columns, and an additional most significant bit R7receiving any carry digit of the addition.

Many multiplier structures, which favor calculation speed, such as theDadda multiplier or Wallace tree multiplier, are designed to perform theoperations shown in FIG. 1 in parallel using combinatory logic. Thenumber of logic gates of these structures increases with the squarenumber of the number of bits of the multiplicands. It may be undesirableto sacrifice this area of silicon for an element that does not require anearly immediate calculation result, as is the case in most built-intest systems.

SUMMARY OF THE INVENTION

It is thus desirable to provide a particularly small multiplier withsufficient performance for use in a BIST device. This desire may beaddressed by a multiplier of a binary number A of n bits by a binarynumber B of p bits, configured to add each term A_(i)B_(j) with a leftshift by i+j bits, where A_(i) is the bit of weight i of number A, andB_(j) the bit of weight j of the number B, with i varying between 0 andn−1, and j varying between 0 and p−1. The multiplier comprises a firstcounter associated with the number A, configured to count modulo n, andpaced by a clock. A second counter is associated with the number B,paced by the clock. The multiplier may also include means or circuitryfor sequentially producing the terms A_(i)B_(j) by taking the contentsof the first and second counters respectively as weights i and j. Themultiplier may also include means or circuitry for shifting the contentof one of the first and second counters by an increment when the othercounter has achieved a revolution.

According to an embodiment, the multiplier comprises, to add the termsA_(i)B_(j), a programmable increment counter of n+p bits, paced by theclock and receiving the current term A_(i)B_(j) as a setpoint to programan increment of 2^(i+j). The programmable increment counter may includea series of cascade-connected flip-flops such that if the programminginput of rank i+j is active, the flip-flop of rank i+j togglessystematically, and any flip-flop of rank k>i+j toggles if theflip-flops of ranks between i+j and k−1 are in an active state.

According to an embodiment, the second counter may be configured tocount modulo p+1, and the multiplier may include means or circuitry forexcluding the current term A_(i)B_(j) when the second counter containsj=p. The second counter may be configured to count modulo p, and themultiplier may include means or circuitry for incrementing the firstcounter by an increment greater than or equal to 2 upon each revolutionof the second counter.

According to an embodiment, the first counter may be configured to countup and the second counter is configured to count down. According to anembodiment, the means or circuitry for producing the terms A_(i)B_(j)may comprise two multiplexers respectively receiving the numbers A andB, and whose select commands are respectively supplied by the first andsecond counters. An AND gate may combining the outputs of themultiplexers.

According to an embodiment, the means or circuitry for excluding theterm A_(i)B_(j) may comprise a gate configured to cancel the term whenthe second counter contains p. According to an embodiment, to excludethe term A_(i)B_(j), the multiplexer associated with number B maycomprise a (p+1)-th input selectable by the content (j) of the secondcounter, and which receives the value 0.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a table illustrating a methodology for multiplying binarynumbers in accordance with the prior art.

FIG. 2 is a schematic diagram of a serial multiplier in accordance withan embodiment of the present invention.

FIG. 3 is a diagram showing a first operating mode of the multiplier inFIG. 2.

FIG. 4 is a diagram showing an alternative operation of the multiplierin FIG. 2.

FIG. 5 is a diagram showing a second operating mode of the multiplier inFIG. 2.

FIG. 6 a is a schematic diagram of an asynchronous programmableincrement counter in accordance with an embodiment of the presentinvention.

FIG. 6 b is a schematic diagram of a synchronous programmable incrementcounter in accordance with an embodiment of the present invention.

FIG. 7 is a diagram showing an operating mode of a multiplier devoid ofphantom cycles in accordance with the present invention.

FIG. 8 is a schematic diagram of a portion of a serial multiplierenabling operation according to the diagram in FIG. 7 and in accordancewith an embodiment of the present invention.

FIG. 9 is a diagram showing a serial multiplier operating mode of amultiplier enabling the number of cycles for a multiplication to bereduced in accordance with the present invention.

FIG. 10 is a schematic diagram of a serial multiplier operatingaccording to the mode of FIG. 9 and in accordance with an embodiment ofthe present invention.

FIG. 11 is a schematic diagram of a portion of a synchronousprogrammable increment counter in accordance with an embodiment of thepresent invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In a BIST device, the calculation speed (e.g. high) of a multiplier maybe relatively unimportant. In most situations, it is possible to merelyprovide a serial multiplier producing a result in at least n² clockcycles, where n is the size of the multiplicands. Even if existingserial structures are particularly simple, the aim is to further reducethe occupied surface area of silicon.

FIG. 2 schematically represents one embodiment of a serial multiplierwith a particularly simple structure. To be more precise, the multiplierhas a parallel-serial structure, as the multiplicands A and B areprovided in parallel, while the partial products A_(i)B_(j) are producedin series. The multiplicands A and B may have different sizes, forexample, respectively n and p bits.

The multiplicands A and B are supplied to respective multiplexers MUX,of n bits to 1 and of p bits to 1. The select inputs of the multiplexersrespectively receive the weights i and j of the bits A_(i) and B_(j) tobe selected in the numbers A and B, where i varies between 0 and n−1,and j varies normally between 0 and p−1. The selected bits A_(i) andB_(i) are combined by an AND gate 10 to produce the current termA_(i)B_(j).

The weight i used to do the selection of the bit A_(i) is supplied by acounter CNT-A configured to count modulo n, while the weight j used todo the selection of the bit B_(j) is supplied by a counter CNT-Bconfigured to count modulo p+1. The counters CNT-A and CNT-B are pacedby a system clock CK and their initial content can be programmed byinitialization lines INIT.

It is noted, with this configuration, that the weight j can reach thevalue p, which is a value not corresponding to any bit of number B,since the maximum weight of the bits of number B may be p−1. However,this possibility is authorized and, when it occurs, the value of thecurrent term A_(i)B_(j) is ignored. To ignore such a term, given thestructure of the multiplier, it is sufficient to cancel it. This isdone, for example, using an AND gate 12 which combines the output ofgate 10 and a masking signal MK, active when the counter CNT-B containsvalue p.

In the example represented, n=p=4. The counter CNT-A is a counter on 2bits, while the counter CNT-B is a counter on 3 bits. The counter CNT-Bcan theoretically count between 0 and 7, but may be configured inpractice to count between 0 and 4. The masking signal MK is then thevalue of the most significant bit MSB of the counter CNT-B. This mostsignificant bit may furthermore not be part of the value j supplied tothe multiplexer, as represented.

According to an alternative, to ignore the term A_(i)B_(j) when theweight j is not within the limits, the multiplexer associated with thenumber B can comprise, as represented in dotted lines, five inputsinstead of four, and the fifth input, that is selected when j=4,receives the value 0 constantly. In this case, as represented in dottedlines, the most significant bit MSB of the counter CNT-B is part of thevalue j supplied to the multiplexer.

Generally speaking, for a number B of p bits and a counter CNT-Bcounting modulo p+1, the multiplexer associated with the number Bcomprises p+1 inputs, the last of which, selected when j=p, receives 0constantly. The terms A_(i)B_(j) produced sequentially by the gate 10are supplied to a demultiplexer 1 towards 7 DMUX. The select input ofthe demultiplexer receives the output of an adder 14 that supplies thesum of the weights i and j of the current term A_(i)B_(j), these weightsbeing respectively supplied by the counters CNT-A and CNT-B.

Therefore, the output line of the demultiplexer towards which thecurrent term A_(i)B_(j) is directed is representative of the left shiftto be performed to sum the term, i.e. of the rank of the column in whichthe term is arranged according to the representation in FIG. 1.

The summation of the terms A_(i)B_(j) is done using a programmableincrement counter CNT-R, paced by the clock CK. The increments areprogrammable by powers of 2. The size in bits of the counter is that n+pof the result R to be produced, i.e. eight bits R0 to R7 in the example.The counter comprises n+p−1=7 increment programming inputs, respectivelyfor the bits R0 to R6, receiving the outputs of the demultiplexer DMUX.

The operation of the counter CNT-R is as follows. When a programminginput of rank k is on 1, the value formed by the bits of rank k andabove is incremented by 1 upon the next active edge of the clock CK,which amounts to incrementing the counter by 2^(k). In theory, severalprogramming inputs can be on 1, but in the structure in FIG. 2, only oneinput is on 1 at once, which occurs when the current term A_(i)B_(j),transmitted on one of the outputs of the demultiplexer DMUX, is on 1.The content of the counter CNT-R remains unchanged when all theprogramming inputs are on 0. With this configuration, each termA_(i)B_(j) is added to the content of the counter CNT-R at the positioni+j, which corresponds to the addition of the term to the content of aregister with a left shift by i+j bits, or even to the addition of theterm after multiplying it by 2^(i+j).

FIG. 3 is a diagram showing a first operating mode of the multiplier inFIG. 2. The counter CNT-A is configured to count up and the counterCNT-B is configured to count down. The initial values of the twocounters are programmed on 0. Therefore, at the pace of the clock CK,and within the framework of the example with n=p=4, the counter CNT-Acounts 0, 1, 2, 3, 0, 1 . . . while the counter CNT-B counts 0, 4, 3, 2,1, 0, 4, 3 . . . .

Upon the first clock cycle CK, the term A₀B₀ is added to the position 0of the counter CNT-R. Upon the second cycle, the counter CNT-B includesthe value 4, which is not within the limits. The term A₁B₄, not beingdefined, is cancelled and the content of the counter CNT-R remainsunchanged. Upon the next two cycles, the terms A₂B₃ and A₃B₂ aresuccessively added to the position 5 of the counter CNT-R, and so on andso forth.

After 20 cycles, all the terms A_(i)B_(j) have been added to thecorresponding positions of the counter CNT-R, which then includes theresult R of the multiplication. It can be seen that the weights i and jof the terms A_(i)B_(j) vary in any way during the clock cycles. Thismay important as the addition is commutative, and the final result isthe same provided that the terms are taken into account with the propershift and are all scanned. These properties are thus used to generatethe sequence of the terms A_(i)B_(j) in a relatively simple way usingtwo simple counters counting continuously.

The price of this relative simplicity is the generation of phantomcycles corresponding to the phases in which the counter CNT-B is notwithin the limits. In the example in FIG. 3, four phantom cycles arecounted, represented in frames, and sixteen useful cycles. For 4-bitnumbers, one cycle in five is a phantom cycle.

By starting the counters of the values 2 and 3, i.e. by starting justafter the first phantom cycle, as represented by a range F1, themultiplication is performed in 19 cycles instead of 20. After the19^(th) cycle, instead of ending on the values 1 and 4, corresponding toa phantom cycle, the counters are forced to their starting values 2 and3. In this case, each multiplication is performed in 19 cycles insteadof 20.

Generally speaking, the proportion of phantom cycles is 1 for eachrevolution of the counter CNT-B, or of the counter that has the greatestnumber of cycles to count. Therefore, this proportion decreases when thenumber of bits of the multiplicands increases. The proportion can befurther decreased by selecting the starting values of the counters justafter a phantom cycle, which enables the number of phantom cycles permultiplication phase to be reduced by 1.

FIG. 4 is a diagram showing an alternative in which the counters CNT-Aand CNT-B start at their default initial values, i.e. the values takenafter a simple reset of the counters. The structure of the counters isthen simplified by the omission of the circuits used to program thestarting values (INIT).

Therefore, upon the first clock cycle, the counters CNT-A and CNT-B havejust been initialized to their default values 0 and 4. The first cycleis a phantom cycle, since the value 4 is not within the limits. Theterms A_(i)B_(j) are then produced according to a sequence differentfrom FIG. 3, but this does not impact the end result given thecommutative property of the addition. The phantom cycles are representedin frames.

In the example in FIGS. 3 and 4, it can be seen that terms with the sameposition i+j in the result R are all produced consecutively, accordingto the sequence of positions 0, 5, 1, 6, 2, 3, 4 in FIG. 3 and accordingto the sequence 4, 0, 5, 1, 6, 2, 3 in FIG. 4. Now, the terms with thesame position in the result need not be produced consecutively, due tothe commutative property of the addition.

FIG. 5 is a diagram showing a second operating mode producing a sequenceof terms according to non-consecutive positions i+j. Here the counterCNT-B is configured to count up, like the counter CNT-A. The countersCNT-A and CNT-B respectively count from 0 to 3 and from 0 to 4.

Upon the first cycle, the counters have been reset and each include thevalue 0. During the first four clock cycles, the contents of thecounters CNT-A and CNT-B vary identically. Upon the fifth cycle, aphantom cycle, the counter CNT-A overruns and comes back to 0, while thecounter CNT-B reaches its maximum value 4, to come back to 0 upon thesixth cycle.

The position in the result of the terms A_(i)B_(j) changes upon eachcycle. This enables two counters of the same nature to be used startingfrom their reset value.

The multiplication is over at the 19^(th) cycle, and the 20^(th) cycleis a phantom cycle. This phantom cycle can thus be removed inconsecutive multiplications by forcing the counters to reset at the endof each 19^(th) cycle.

FIG. 6 a schematically represents one embodiment of a programmableincrement counter CNT-R. This embodiment is shown based on anasynchronous counter architecture.

An asynchronous counter comprises a series of cascade-connected Tflip-flops, the clock input of each flip-flop receiving the Q/ invertedoutput of the previous flip-flop. The clock input of the first flip-flopreceives the counting clock, and each flip-flop receives the value 1 atits toggle input T. With this configuration, each flip-flop togglesevery time the Q/ output of the previous flip-flop has a rising edge,i.e. when the previous flip-flop toggles from 1 to 0.

In FIG. 6 a, the counter comprises as many flip-flops (R₀-R₇) as bits inthe result R of the multiplication. The clock input of each flip-flop ispreceded by a multiplexer that selects either the Q/ output of theprevious flip-flop or the clock signal CK. The multiplexer associatedwith the first flip-flop R0 receives the value 0 instead of the Q/output of a flip-flop.

The selection commands of the multiplexers are the increment programminginputs connected to the outputs of the demultiplexer DMUX in FIG. 2.When a programming input is on 0, the multiplexer selects the Q/ outputof the previous flip-flop according to a traditional asynchronouscounter configuration. For the first flip-flop, the multiplexer selectsthe value 0. Therefore, if all the programming inputs are on 0, thecounter does not receive any clock signal and keeps its content.

When a programming input of rank k is on 1, the multiplexer directs theclock CK towards the flip-flop R_(k). Therefore, if only thisprogramming input is on 1, the others being on 0, the flip-flops R_(k)to R₇ act like an 8-k-bit counter that is incremented upon the netfalling edge of the clock CK, while the flip-flops R₀ to R_(k−1) arefixed.

FIG. 6 b schematically represents one embodiment of a programmableincrement counter with a synchronous structure. A synchronous countercomprises a series of T flip-flops paced simultaneously by a same clockCR. The toggle input T of each flip-flop is connected to be active onlyif all the lower-ranking flip-flops are on 1. This is achieved by aseries of cascade-connected AND gates 15. Each AND gate controls the Tinput of an associated flip-flop and combines the Q output of theprevious flip-flop with the output of the previous AND gate. The T inputof the first flip-flop normally receives the value 1 continuously, andthe AND gate preceding the second flip-flop is thus optional.

To make the increment programmable, an OR gate is provided between eachAND gate 15 and the T input of the associated flip-flop. A first inputof the OR gate receives the output of the AND gate, and a second inputof the OR gate forms an increment programming input, the rank of whichis the one of the associated flip-flop. With this configuration, when aprogramming input of rank k is put to 1, the OR gate forces to 1 the Tinput of the flip-flop of rank k. The flip-flop then toggles upon eachclock edge independently of the states of the lower-ranking flip-flops,incrementing the content of the counter by 2^(k) upon each cycle.

The T input of the first flip-flop directly receives the programminginput of rank 0. The diagrams in FIGS. 3-5 show that, to generate thesequence of the weights i and j of the terms A_(j)B_(j), it issufficient to take the contents of two counters that count continuously,respectively modulo n and p, by shifting the content of one of thecounters by one step every time the other counter has done a revolution.

In the previous examples, the content of the counter CNT-B is shiftedupon each revolution due to the fact that it counts one step more perrevolution. The same effect could be obtained with a counter CNT-B thatcounts modulo p instead of p+1, but that is stopped for one cycle aftereach revolution. In this case, in FIG. 5, the sequence 0, 1, 2, 3, 3, 0. . . is obtained for the counter CNT-B. This amounts to decrementingthe counter CNT-B by 1 upon each revolution. These two alternativesproduce phantom cycles.

FIG. 7 is an operating diagram resulting from a transformation of thediagram in FIG. 5, enabling the phantom cycles to be removed. Thecounter CNT-B is here configured to count up modulo p (4 in theexample), instead of counting modulo p+1.

The shifting by one step between the counters upon each revolution isobtained in the following manner, for example. Every time the counterCNT-B reaches its maximum value p−1, the counter CNT-A is incremented by2 instead of 1 upon the next cycle for a single cycle. The phantom cycleexisting in the diagram in FIG. 5 is thus skipped.

In fact, it may not be desirable to set the threshold to p−1 to triggerthe one-step shift. It is sufficient for the counter CNT-B to have donea revolution which can start at any value between 0 and p−1.

Furthermore, the increment used for the shift can be different from 2.The set of values that the increment can take depends on the propertiesof the operands. When the operands have an equal number of bits, theincrement can take as a value any whole number Ic ranging between 2 andp−1, such that Ic−1 and p are prime to each other. The possible valuesof the increment Ic are summarized in the following table for examplesof operand sizes.

Operand size Possible values for Ic 4 bits 2 5 bits 2, 3, 4 6 bits 2 7bits 2, 3, 4, 5, 6 8 bits 2, 4, 6 9 bits 2, 3, 5, 6, 8 10 bits 2, 4, 816 bits 2, 4, 6, 8, 10, 12, 14

Those skilled in the art will be able to find definition sets for theincrement Ic when the operands have different sizes.

FIG. 8 schematically and partially represents one embodiment of a serialmultiplier enabling this operation to be obtained. The structure of thismultiplier is based on that of FIG. 2. Similar elements are referred toby the same references.

The counter CNT-B is configured to count up modulo p instead of p+1. Themasking circuit shown in FIG. 2, formed by the gate 12 controlled by amasking signal MK, is no longer found.

The counter CNT-A is a programmable increment counter. It could have thesame structure as that of FIG. 6 a. In practice, only the programminginputs of ranks 0 and 1, enabling, respectively, a step +1 and a step +2to be selected for the increments are desired. Therefore, the counterhas a classic structure from its third flip-flop, if more than 2 bitsare needed for the counter.

A comparator 16 observes the output j of the counter CNT-B. When j isequal to p−1 (3 in the example), the comparator programs the increment+2 of the counter CNT-A. When j is different from p−1, i.e. in all theother cases, the comparator programs the increment +1 of the counterCNT-A.

The serial multiplier embodiments described herein do a multiplicationin n×p cycles, where n and p are the respective sizes of the operands Aand B. When the sizes are equal and a power of 2, it may be possible todivide the number of cycles by 2 by increasing the surface area of thecircuit according to an acceptable compromise.

To do so, provision is made to produce two distinct simultaneoussequences of terms A_(i)B_(j) and to sum them two by two. The firstsequence, noted A_(i)B_(j), is produced directly by the counters CNT-Aand CNT-B, and the second sequence, noted A_(i)/B_(j/) is produced bythe complements of the counters CNT-A and CNT-B. In addition, the mannerof shifting the counter CNT-A is changed so that all the terms to besummed are produced without any duplications or missing terms.

FIG. 9 is a diagram showing an example of producing suitable sequencesfor 4-bit operands. Starting from the diagram in FIG. 7, the counterCNT-A, in addition to being incremented by 2 upon each revolution of thecounter CNT-B, is further incremented by 2 upon each mid-revolution ofthe counter CNT-B. In other words, for 4-bit operands, the counter CNT-Ais incremented by 2 every time the content of the counter CNT-B has anodd value.

The diagram indicates the resulting sequences for the values i+j, i/+j/,and the complements CNT-A/, CNT-B/, of the counters CNT-A and CNT-B. Itcan be seen that all the combinations of the pairs (i, j) arerepresented over 8 cycles in the values taken by the counters or theircomplements.

FIG. 10 schematically represents one embodiment of a multiplieroperating according to the mode of FIG. 9. The structure in FIG. 8 isfound again twice. A first set of multiplexers MUX, AND gate 10, anddemultiplexer DMUX is associated with the direct contents of thecounters CNT-A and CNT-B, supplied by the Q outputs of the flip-flopsforming these counters. A second set of multiplexers MUX′, AND gate 10′,and demultiplexer DMUX′ is associated with the complements of thecontents of the counters CNT-A and CNT-B, supplied by the Q/ outputs ofthe flip-flops forming these same counters.

The demultiplexers DMUX, DMUX′ are respectively controlled by the valuesi+j and i/+j/, produced respectively by the adder 14 and an adder 14′receiving the complements of the contents of the counters CNT-A andCNT-B. The sum of the two numbers formed by the outputs of thedemultiplexers is used to program the increment of the counter CNT-R. Inthe example, two 6-bit numbers are summed, which may require, in theory,a comprehensive 6-bit adder. In reality, given the special structureused, it transpires that a simple OR gate is sufficient to add the mostsignificant bits and the least significant bits. Indeed, as shown in thediagram in FIG. 9, in most cycles, the ranks of the outputs of the twodemultiplexers, defined by the values i+j and i/+j/, are different. Theresult is that an inevitably zero bit is added to a possibly non-zerobit, which only requires a simple OR gate.

It is for the central rank, 3 in the example, that two bits which canboth be on 1 are summed. To do so, a semi-adder formed, as represented,by an OR-exclusive gate and an AND gate, each receiving the outputs ofrank 3 of the two demultiplexers, is provided. The OR-exclusive gatesupplies the bit of rank 3 of the sum and the AND gate supplies a carrydigit. The bit of rank 4 of the sum is formed by an OR of the outputs ofrank 4 of the two demultiplexers, followed by an OR with the carrydigit. There is no other carry digit to be taken into account as, if thesemi-adder produces a carry digit, this means that all the outputs ofthe demultiplexers, except those of rank 3, are zero.

The comparator 16, which determines the value of the increment to beapplied to the counter CNT-A, is configured to compare the content ofthe counter CNT-B with the values 1 and 3, i.e. the median value and themaximum value of the content of the counter. With this structure, theincrement programmed for the counter CNT-R can be of any type, anddifferent from a power of 2. In other words, several incrementprogramming inputs can be simultaneously on 1. The counter structures inFIGS. 6 a and 6 b may not work in such a situation.

FIG. 11 partially represents one embodiment of a programmable incrementcounter enabling any number of programming inputs to be put to 1. Thiscounter has a synchronous architecture, like the one in FIG. 6 b, i.e.the toggle input T of a flip-flop is only active, normally, if all thelower-ranking flip-flops are on 1.

In addition, a logic cell 18 is associated with each flip-flop to both“request” a toggle from the next cell through an AND gate 20 and decideto toggle the current flip-flop through an XOR gate 22, the output ofwhich is connected to the T input of the flip-flop. A toggle “request”is equivalent, in a conventional synchronous counter, to the indicationthat all the lower-ranking flip-flops are at “1” and thus that the nextflip-flop must toggle. In the structure of FIG. 11, it is furtherdetermined, according to the programming input, whether the currentflip-flop is effectively toggled and whether the toggle request ispropagated.

The cell 18 is configured to toggle the associated flip-flop upon thenext clock edge CK, if one of the following conditions is met:

a) The programming input is at 0 and the previous cell requests thetoggle of the flip-flop (case of the conventional synchronous counter).

b) The programming input is at 1, and the previous cell does not requestthe toggle of the flip-flop (case of the counter in FIG. 6 b with asingle programming input at 1).

This functionality is obtained using the XOR gate 22, a first input ofwhich is connected to the programming input, and a second input of whichreceives the output of the AND gate 20 of the previous cell.

The cell 18 is further configured to freeze the flip-flop if one of thefollowing conditions is met:

c) The programming input is at 0 and the previous cell does not requestthe toggle of the flip-flop (case of the conventional synchronouscounter).

d) The programming input is at 1, and the previous cell requests thetoggle of the flip-flop. In other words, if the toggle is “requested”twice, the flip-flop does not toggle, which in fact amounts to togglingthe flip-flop twice. This occurs when a lower-ranking flip-flop has itsprogramming input at 1.

This functionality is also obtained using the XOR gate 22. A togglerequest is produced by the AND gate 20 in the following cases:

e) In case a) when the flip-flop contains 1.

f) In case b) when the flip-flop contains 1.

g) In case d), independently of the content of the flip-flop. It isassumed that the flip-flop has toggled twice even though it was frozen.If it includes 0, this means that the flip-flop transitioned to 1(virtually) and that a corresponding toggle request must be propagated.

The functions e) and f) are obtained by an OR gate 24 combining thetoggle request of the previous cell and the programming input. A firstinput of the AND gate 20 receives the output of gate 24, and a secondinput receives the Q output of the flip-flop.

The function g) is obtained by an AND gate 26 combining the togglerequest of the previous cell and the programming input. An OR gate 28 isinserted between the Q output of the flip-flop and gate 20, and forcesthe second input of gate 20 to 1 when the output of gate 26 is active.

1-9. (canceled)
 10. A multiplier for multiplying a binary number A of nbits by a binary number B of p bits and configured to add each termA_(i)B_(j) with a left shift by i+j bits, where A_(i) is a bit of weighti of the binary number A, and B_(j) a bit of weight j of the binarynumber B, with i varying between 0 and n−1, and j varying between 0 andp−1, the multiplier comprising: a first counter associated with thebinary number A and configured to count modulo n and be clocked by aclock; a second counter associated with the binary number B andconfigured to be clocked by the clock; switching circuitry configured tosequentially produce terms A_(i)B_(j) by at least defining the weights iand j based upon contents of said first and second countersrespectively; and shifting circuitry configured to shift the content ofone of said first and second counters by an increment when the other ofsaid first and second counters has executed a revolution.
 11. Themultiplier according to claim 10, further comprising, to add the termsA_(i)B_(j), a programmable increment counter of n+p bits and configuredto be clocked by the clock and receive a current term A_(i)B_(j) as asetpoint to program an increment of 2^(i+j).
 12. The multiplieraccording to claim 11, wherein said programmable increment countercomprises a series of cascade-connected flip-flops configured to, if theprogramming input of rank i+j is active, toggle the flip-flop of ranki+j systematically, and toggle any flip-flop of rank k>i+j if flip-flopsof ranks between i+j and k−1 are active.
 13. The multiplier according toclaim 10, wherein said second counter is configured to count modulo p+1;and wherein the multiplier further comprises logic circuitry configuredto exclude a current term A_(i)B_(j) when said second counter has thebit weight j being equal to the bit weight p.
 14. The multiplieraccording to claim 10, wherein said second counter is configured tocount modulo p; and wherein said shifting circuitry is configured toincrement said first counter by an increment greater than or equal to 2upon each revolution of said second counter.
 15. The multiplieraccording to claim 10, wherein said first counter is configured to countup and wherein said second counter is configured to count down.
 16. Themultiplier according to claim 10, wherein said switching circuitryfurther comprises: two multiplexers configured to respectively receivethe binary numbers A and B, and to receive select commands respectivelyfrom said first and second counters, said two multiplexers each having arespective output; and an AND gate configured to combine the outputs ofsaid two multiplexers.
 17. The multiplier according to claim 13, whereinsaid logic circuitry comprises a logic gate configured to cancel theterm A_(i)B_(j) when said second counter includes p.
 18. The multiplieraccording to claim 16 wherein, one of said two multiplexers associatedwith the binary number B comprises a (p+1)-th input receiving a value 0and configured to be selectable based upon the content of said secondcounter.
 19. A multiplier for multiplying a binary number A of n bits bya binary number B of p bits and configured to add each term A_(i)B_(j)with a left shift by i+j bits, where A_(i) is a bit of weight i of thebinary number A, and B_(j) a bit of weight j of the binary number B, themultiplier comprising: a first counter associated with the binary numberA; a second counter associated with the binary number B; switchingcircuitry configured to sequentially produce terms A_(i)B_(j) by atleast defining the weights i and j based upon contents of said first andsecond counters respectively; and shifting circuitry configured to shiftthe content of one of said first and second counters when the other ofsaid first and second counters has executed a revolution.
 20. Themultiplier according to claim 19, wherein said first counter isconfigured to count modulo n; and wherein said multiplier furthercomprises, to add the terms A_(i)B_(j), a programmable increment counterof n+p bits and configured to operate based upon a clock and program anincrement of 2^(i+j) based upon a current term A_(i)B_(j).
 21. Themultiplier according to claim 20, wherein said programmable incrementcounter comprises a series of cascade-connected flip-flops configuredto, if the programming input of rank i+j is active, toggle the flip-flopof rank i+j, and toggle any flip-flop of rank k>i+j if flip-flops ofranks between i+j and k−1 are active.
 22. The multiplier according toclaim 19, wherein said second counter is configured to count modulo p+1;and wherein the multiplier further comprises logic circuitry configuredto exclude a current term A_(i)B_(j) when said second counter has thebit weight j being equal to the bit weight p.
 23. The multiplieraccording to claim 19, wherein said second counter is configured tocount modulo p; and wherein said shifting circuitry is configured toincrement said first counter by an increment greater than or equal to 2upon each revolution of said second counter.
 24. The multiplieraccording to claim 19, wherein said first counter is configured to countup and wherein said second counter is configured to count down.
 25. Themultiplier according to claim 19, wherein said switching circuitryfurther comprises: two multiplexers configured to respectively receivethe binary numbers A and B, and to receive select commands respectivelyfrom said first and second counters, said two multiplexers each having arespective output; and an AND gate configured to combine the outputs ofsaid two multiplexers.
 26. The multiplier according to claim 22, whereinsaid logic circuitry comprises a logic gate configured to cancel theterm A_(i)B_(j) when said second counter includes p.
 27. The multiplieraccording to claim 25 wherein, one of said two multiplexers associatedwith the binary number B comprises a (p+1)-th input configured to beselectable based upon the content of said second counter.
 28. A methodof multiplying a binary number A of n bits by a binary number B of pbits and by adding each term A_(i)B_(j) with a left shift by i+j bits,where A_(i) is a bit of weight i of the binary number A, and B_(j) a bitof weight j of the binary number B, the method comprising: usingswitching circuitry to produce terms A_(i)B_(j) by at least defining theweights i and j based upon contents of first and second countersrespectively, the first and second counters being associated with thebinary number A and the binary number B, respectively; and usingshifting circuitry to shift the content of one of the first and secondcounters when the other of the first and second counters has executed arevolution.
 29. The method according to claim 28, wherein the firstcounter counts modulo n; and wherein the method further comprises, toadd the terms A_(i)B_(j), operating a programmable increment counter ofn+p bits based upon a clock and program an increment of 2^(i+j) basedupon a current term A_(i)B_(j).
 30. The method according to claim 29,wherein operating the programming increment counter comprises operatinga series of cascade-connected flip-flops to, if the programming input ofrank i+j is active, toggle the flip-flop of rank i+j, and toggle anyflip-flop of rank k>i+j if flip-flops of ranks between i+j and k−1 areactive.
 31. The method according to claim 28, wherein the second countercounts modulo p+1; and wherein the method further comprises using logiccircuitry to exclude a current term A_(i)B_(j) when the second counterhas the bit weight j being equal to the bit weight p.
 32. The methodaccording to claim 28, wherein the second counter is configured to countmodulo p; and wherein using the shifting circuitry comprisesincrementing the first counter by an increment greater than or equal to2 upon each revolution of the second counter.
 33. The method accordingto claim 28, wherein using the switching circuitry further comprises:using two multiplexers to respectively receive the binary numbers A andB, and receive select commands respectively from the first and secondcounters; and combine outputs of the two multiplexers using an AND gate.34. A multiplier for multiplying a binary number A of n bits by a binarynumber B of p bits and configured to add each term A_(i)B_(j) with aleft shift by i+j bits, where A_(i) is a bit of weight i of the binarynumber A, and B_(j) a bit of weight j of the binary number B, with ivarying between 0 and n−1, and j varying between 0 and p−1, themultiplier comprising: a first counter associated with the binary numberA and connected to be clocked by a clock; a second counter associatedwith the binary number B; switching circuitry configured to sequentiallyproduce terms A_(i)B_(j) by at least defining the weights i and j basedupon contents of said first and second counters respectively; and foradding the terms A_(i)B_(j), a programmable increment counter of n+pbits, configured to be clocked by the clock and receive a current termA_(i)B_(j) as a setpoint to program an increment of 2^(i+j).
 35. Themultiplier according to claim 34, wherein said programmable incrementcounter comprises a series of cascade-connected flip-flops configuredto, if the programming input of rank i+j is active, toggle the flip-flopof rank i+j systematically, and toggle any flip-flop of rank k>i+j ifflip-flops of ranks between i+j and k−1 are active.
 36. The multiplieraccording to claim 34, wherein the second counter is configured to countmodulo n and is clocked by the clock, the multiplier further comprisingshifting circuitry configured to shift the content of one of said firstand second counters by an increment when the other of said first andsecond counters has executed a revolution.
 37. The multiplier accordingto claim 36, wherein said second counter is configured to count modulop+1; and wherein the multiplier further comprises logic circuitryconfigured to exclude a current term A_(i)B_(j) when said second counterhas the bit weight j being equal to the bit weight p.
 38. The multiplieraccording to claim 36, wherein said second counter is configured tocount modulo p; and wherein said shifting circuitry is configured toincrement said first counter by an increment greater than or equal to 2upon each revolution of said second counter.
 39. The multiplieraccording to claim 36, wherein said first counter is configured to countup and wherein said second counter is configured to count down.
 40. Themultiplier according to claim 34, wherein said switching circuitryfurther comprises: two multiplexers configured to respectively receivethe binary numbers A and B, and to receive select commands respectivelyfrom said first and second counters, said two multiplexers each having arespective output; and an AND gate configured to combine the outputs ofsaid two multiplexers.
 41. The multiplier according to claim 37, whereinsaid logic circuitry comprises a logic gate configured to cancel theterm A_(i)B_(j) when said second counter includes p.
 42. The multiplieraccording to claim 40 wherein, the multiplexer associated with thebinary number B comprises a (p+1)-th input receiving a value 0 andconfigured to be selectable based upon the content of said secondcounter.